Draft v1.0 — 2026-08-06
Status: Open for feedback. Read the paper → open an issue.
Paper:paper.md
When a causal agent models its own model-generation mechanism, it hits a limit. Not "AI can't understand itself"—but rather: self-modeling creates a spectrum of certification difficulty, measured by a parameter ρ (the reflection rank).
This paper connects three research traditions that rarely talk to each other:
- Computability (Gödel, Rice, Löb): what formal systems can prove about themselves
- Causal inference (Pearl, CHT): what causal queries a model can answer
- Thermodynamics (Landauer, Bennett): what physical cost information erasure incurs
The core finding: they're all describing the same structure in different languages. The reflection rank ρ maps cleanly across all three.
- R-SCM: A Reflective Structural Causal Model—extending Pearl's framework with a G-node for self-modeling
- Reflection Rank ρ: A proof-theoretic parameter measuring how many layers of logical reflection an agent needs to internally certify its own causal correctness
- Full spectrum: ρ = 0 (certifiable) → 1, 2, ... → ω (compressible infinite) → ∞ (divergent)
- Thermodynamic cost: ρ maps directly to Bennett entropy cost via logical irreversibility of the G-node's update function
- Translation table: 8-row Rosetta Stone mapping core concepts across computability, causality, and thermodynamics
- Computability theorists: The Rice theorem application to causal semantics + Feferman tower construction
- Causal inference researchers: An extension of Pearl's SCM (R-SCM) and CHT boundary analysis
- Embedded agency / AI safety: A quantitative framework for self-model certification limits
- Physics of computation: A new source of logical irreversibility—undecidable self-certification
This is a draft seeking critical feedback. Open an issue, or reach out directly.
Topics where input is especially valuable:
- Rice→FC reduction: is the non-trivial semantic property argument watertight?
- G-node Absorption Theorem: does it hold under all standard SCM interpretations?
- Spectrum Theorem (Open Problem 1): for any recursive ordinal α, does an agent with ρ=α exist?
- f_G non-injectivity proof: is the step from undecidability to non-injectivity rigorous?
TBD. For now, link to this repo.
CC BY 4.0